ORIGINAL PAPER
Modelling of Equivalent Mass and Rigidity of Continual Segment of the Inter-Resonance Vibration Machine
 
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1
Department of Mechanics and Automation of Mechanical Engineering Institute of Engineering Mechanics and Transport, Lviv Polytechnic National University, 1 Profesorska St., Lviv, 79013, Ukraine
 
2
Department of Strength of Materials and Structural Mechanics, Institute of Civil Engineering and Building Systems, Lviv Polytechnic National University, 6 Karpinskoho St., Lviv, 79013, Ukraine
 
3
Department of Mechanical Engineering Technologies, Institute of Engineering Mechanics and Transport, Lviv Polytechnic National University, 1 Profesorska St., Lviv, 79013, Ukraine
 
4
Department of Project Management and Occupational Safety, Faculty of Mechanic and Power Engineering, Lviv National Agrarian University, Lviv-Dubliany, 80381, Ukraine
 
 
Online publication date: 2021-06-22
 
 
Publication date: 2021-06-01
 
 
International Journal of Applied Mechanics and Engineering 2021;26(2):70-83
 
KEYWORDS
ABSTRACT
The article deals with a continual segment of an inter-resonance vibration machine. In the form of a solid with distributed parameters this segment combines two defining parameters, namely: the inertial parameter of reactive: masses and appropriate rigidity of elastic coupling. These operation factors are revealed only in dynamic processes and are clearly not included in the parameters of the continual segment. Analytical dependences are developed for modeling of defining parameters of an inter-resonance system, namely: reactive mass and appropriate rigidity of elastic: coupling. Parameters of the reference point of the continual segment passing through its center of velocity are studied. The inertial parameter of the reactive mass and the rigidity of elastic coupling were modeled by the Rayleigh-Ritz method. The reliability of the results of theoretical research was confirmed experimentally and the parameters of the partial frequency of the continual segment were determined.
 
REFERENCES (27)
1.
Lanets O.S., Derevenko I.A., Borovets V.M., Kovtonyuk M.M., Komada P., Mussabekov K. and Yeraliyeva B. (2019): Substantiation of consolidated inertial parameters of vibrating bunker feeder.– Przegląd Elektrotechniczny, vol.95, No.4, pp.47-52.
 
2.
Gursky V.M., Kuzio I.V., Lanets O.S., Kisała P., Tolegenova A. and Syzdykpayeva A. (2019): Implementation of dual-frequency resonant vibratory machines with pulsed electromagnetic drive.– Przegląd Elektrotechniczny, vol.95, No.4, pp.41-46.
 
3.
Sharma A.K., Sharma P., Chauhan P.S. and Bhadoria S.S. (2018): Study on harmonic analysis of functionally graded plates using fem.– International Journal of Applied Mechanics and Engineering, vol.23, No.4, pp.941-961.
 
4.
Jaworski J. W. and Dowell E. H. (2008): Free vibration of a cantilevered beam with multiple steps: comparison of several theoretical methods with experiment.– Journal of Sound and Vibration, vol.312, No.4-5, pp.713-725.
 
5.
Raju L.S., Raju K. and Rao G.V. (1976): Large amplitude free vibrations of tapered beams.– AIAA Journal, vol.14, No.2, pp.280-282.
 
6.
Gharaibeh M.A., Obeidat A.M. and Obaidat M.H. (2018): numerical investigation of the free vibration of partially clamped rectangular plates.– International Journal of Applied Mechanics and Engineering, vol.23, No.2, pp.385-400.
 
7.
Srinivasa C.V., Suresh Y.J. and Prema Kumar W.P. (2014): Experimental and finite element studies on free vibration of skew plates.– International Journal of Applied Mechanics and Engineering, vol.19, No.2, pp.365-377.
 
8.
Jaroszewicz J. (2017): Natural frequencies of axisymmetric vibrations of thin hyperbolic circular plates with clamped edges.– International Journal of Applied Mechanics and Engineering, vol.22, No.2, pp.451-457.
 
9.
Zur K.K. (2015): Green’s function in frequency analysis of circular thin plates of variable thickness.– Journal of Theoretical and Applied Mechanics, vol.53, No.4, pp.873-884.
 
10.
Amabili M. and Carra S. (2012): Experiments and simulations for large-amplitude vibrations of rectangular plates carrying concentrated masses.– Journal of Sound and Vibration, vol.331, No.1, pp.155-166.
 
11.
Buchacz A. (2009): Calculation of flexibility of vibrating beam as the subsystem of mechatronic system by means the exact and approximate methods.– Proceedings in Applied Mathematics and Mechanics, vol.9, No.1, pp.373-374.
 
12.
Buchacz A. (2011): The supply of formal notions to synthesis of the vibrating discrete-continuous mechatronic systems.– Journal of Achievements in Materials and Manufacturing Engineering, International OCOSCO World Press, vol. 44, No.2, pp.168-178.
 
13.
Clementi F., Demeio L., Mazzilli C.E.N. and Lenci S. (2015): Nonlinear vibrations of non-uniform beams by the MTS asymptotic expansion method.– Continuum Mech. Thermodyn, vol.27, pp.703-717.
 
14.
Firouz-Abadi R.D., Haddadpour H. and Novinzadeh A.B. (2007): An asymptotic solution to transverse free vibrations of variable-section beams.– Journal of Sound and Vibration, vol.304, pp.530-540.
 
15.
Ece M.C., Aydogdu M. and Taskin V. (2007): Vibration of a variable cross-section beam.– Mechanics Research Communications, vol.34, No.1, pp.78-84.
 
16.
Mahmoud B., Iman P. and Mahdi B. (2011): Analytical study on the vibration frequencies of tapered beams.– Latin Ameriacan Journal of Solids and Structures, vol.8. pp.149-162.
 
17.
Kisa M. and Gurel M. A. (2007): Free vibration analysis of uniform and stepped cracked beams with circular cross sections.– International Journal of Engineering Science, vol.45, No.2-8, pp.364-380.
 
18.
Lee B.K., Lee J.K., Lee T.E. and Kim S.G. (2002): Free vibrations of tapered Beams with general boundary condition.– (KSCE) Journal of Civil Engineering, vol.6, No.3, pp.283-288.
 
19.
Shin Y. J., Kwon K. M. and Yun J. H. (2008): Vibration analysis of a circular arch with variable cross section using differential transformation and generalized differential quadrature.– Journal of Sound and Vibration, vol.309, No.1-2, pp.9-19.
 
20.
Lee J.W. (2016): Free vibration analysis using the transfer-matrix method on a tapered beam.– Journal of Computers and Structures, vol.164, pp.75-82.
 
21.
Vescovini R., Dozio L., D’Ottavio M. and Polit O. (2018): On the application of the Ritz method to free vibration and buckling analysis of highly anisotropic plates.– Composite Structures, vol.192, pp.460-474.
 
22.
Dozio L. (2011): On the use of the trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates.– Thin-Walled Structures, vol.49, No.1, pp.129-144.
 
23.
Yuan J. and Dickinson S. M. (1992): The flexural vibration of rectangular plate systems approached by using artificial springs in the Rayleigh-Ritz method.– Journal of Sound and Vibration, vol.159, No.1, pp.39-55.
 
24.
Kumar Y. (2018): The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review.– Journal of Vibration and Control, vol.24, No.7, pp.1205-1227.
 
25.
Rahbar-Ranji A. and Shahbaztabar A. (2016): Free vibration analysis of moderately thick rectangular plates on Pasternak foundation with point supports and elastically restrained edges by using the Rayleigh–Ritz method.– Journal of Failure Analysis and Prevention, vol.16, pp.1006–1023.
 
26.
Mazanoglu K. (2017): Natural frequency analyses of segmented Timoshenko–Euler beams using the Rayleigh– Ritz method.– Journal of Vibration and Control, vol.23, No.13, pp.2135-2154.
 
27.
Babakov I. М. (1968): Theory of Vibration.– Leningrad, Nauka.
 
eISSN:2353-9003
ISSN:1734-4492
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